Transport, stirring and mixing in two-dimensional vortex flows

Citation

Min, Inki A. (1995) Transport, stirring and mixing in two-dimensional vortex flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8y2c-8203. https://resolver.caltech.edu/CaltechETD:etd-10182007-132306

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

To understand the basic contribution of vortex motion in the transport and mixing of passive fluid, we study a system of N discrete vortices. With variation of N and [...] (a vorticity distribution parameter), we are able to experiment with a range of vortex dynamics sufficient to capture many of the features of two-dimensional turbulence in their elementary form - such as vortex merging (inverse cascade of energy), filamentation (enstrophy cascade), etc. With this model the mixing of the fluid is numerically studied via stretch statistics and the spatial distribution of a non-diffusive scalar interface. The spectrum of spatial distribution of scalars as a result of the stirring motion of the N vortices is particularly important in view of the recent (as well as historical) interest in the characterization of the scalar distribution in turbulence. We also examine the velocity field statistics and the Lagrangian motion of fluid particles. It is also instructive to look at the kinematic causes behind the types of statistics that are obtained for the velocity structure functions. A 'building block' approach to understanding these effects in turbulence may lie in building up from a collection of discrete vortices, as done in this thesis, to adding vortices of different scales and the three-dimensional effects. It is in the context of these wider issues that we study the N-vortex problem.

In the final part of this thesis we investigate the two-dimensional mixing produced by large scale vortical structures during the evolution of a spatially developing mixing layer. Although the advent of three-dimensionality and fully developed turbulence are essential features of mixing layers, it is still dominated by the large scale two-dimensional structures and its effect on the mixing is illustrated here.

Thesis Files